On Controlling an Uncertain System With Polynomial Chaos and H2 Control Design

Author:

Templeton Brian A.1,Cox David E.2,Kenny Sean P.2,Ahmadian Mehdi1,Southward Steve C.3

Affiliation:

1. Center for Vehicle Systems and Safety, Virginia Tech, Blacksburg, VA 24061

2. Dynamic Systems and Control Branch, NASA Langley Research Center, Hampton, VA 23681

3. Center for Vehicle Systems and Safety, Virginia Tech, Danville, VA 24540

Abstract

AbstractThis paper applies the H2 norm along time and parameter domains. The norm is related to the probabilistic H2 problem. It is calculated using polynomial chaos to handle uncertainty in the plant model. The structure of expanded states resulting from Galerkin projections of a state space model with uncertain parameters is used to formulate cost functions in terms of mean performances of the states, as well as covariances. Also, bounds on the norm are described in terms of linear matrix inequalitys. The form of the gradient of the norm, which can be used in optimization, is given as a Lyapunov equation. Additionally, this approach can be used to solve the related probabilistic LQR problem. The legitimacy of the concept is demonstrated through two mechanical oscillator examples. These controllers could be easily implemented on physical systems without observing uncertain parameters.

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Reference27 articles.

1. The Homogeneous Chaos;Wiener;Am. J. Math.

2. Optimal Operation of Soil Aquifer Treatment Systems Considering Parameter Uncertainty;Xu;Water Resour. Manage.

3. The Orthogonal Development of Nonlinear Functionals in Series of Fourier–Hermite Functionals;Cameron;Ann. Math.

4. The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations;Xiu;SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.

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